Question: Rewrite as a simplified fraction. ${3.13\overline{4} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3134.4444...\\ 100x &= 313.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2821}$ ${x = \dfrac{2821}{900}} \text{or} {3 \dfrac{121}{900}}$